I am trying to find free research information on the market for:

Childrens Web Sites
Childrens Educational Web Sites
Children's Entertainment Web Sites

Chidren (for my purposes is defined as ages 3-8)

The market information I'm trying to identify is:
- market size (# of users, demographics (age, sex, etc.))
- market value (revenue)
- most successful sites in these categories
- anticipated growth in this space

Dear Imam, 

I have found this report - Research and Guidelines for Children's Use
of the Internet  - www.nsbf.org/safe-smart/full-report.htm  - from
which you may be able to draw some statistics.

I would provide a full answer when I have one, take this one as an
appetizer.

Excellent report.  Has some of the info I'm seeking. I'm curious, I
can't seem to find any info on when the report was done.

I meant to add to the last comment:

One of the most important elements of what I'm looking for is some
sort of revenue number associated with my target age group.

Revenue from sites that provide content to this age group
specifically subscription sites for kids.

You may find it difficult to find much info on subscription (ie
newsletters) for children under 13. From what I understand it is
illegal in the United States to ask for the email address of a person
under 13. So they will have to very carefully ask for parents
permission if they do this at all. This is not really my area of
expertise or I might know more about this. I am not sure if they try
to confirm age or ask for the parents to relese this. Good Luck.